My actual question is at the end of the post, the beginning is just an intro to my situation, so skip ahead if you want

First, I know how apertures and DOF works. I've learned the basics first, and then more by actually going out and shooting. I've shot for maybe 2-3 years, but only recently I've really gotten into photography as a serious-ish hobby.

Now, I've sometimes tried to explain how photography and cameras/lenses work to my friends (regardless if they've asked or not, I'm afraid :P), and I've found it's pretty difficult to explain if they have no interest in the theories of photography. I started thinking about some of these things myself, and found that a lot of what I've learned is often taught in the form of "you will get more depth of field if you use a narrower aperture", which is great, you don't really need to make it more complicated for a beginning photographer. I know how it works, but I can't even explain it to myself, which is strange :).

However, thinking about this very fact, I started wondering, why? Why do I get more depth of field? I haven't thought about this as all the tutorials I've read on the subject don't go farther than this. I know how my eye works, if I bring a spoon close to my eye, it starts getting blurrier because my eye can't focus any closer. I also basically know why this is. I also know that a wide aperture gathers more light at a time than a narrow one, basic stuff, right?

I once saw it being compared to throwing a bucket of paint onto a canvas (large aperture, lots of background blur) or dripping the paint through a straw (small aperture, details). Not the exact comparison but the idea was the same. I find it's a good visualisation, but still, why couldn't you use a thousand straws at the same time to get the same aperture that you get with the bucket (equal to using a large aperture that gets a deep DOF)?

Now, to my question:

Does the sensor need more light and time to "paint" more details in the final picture? A camera doesn't know what it's shooting, but still it can only resolve a limited area with a large aperture. Why, if I want a rock in the foreground and the beach behind to all be sharp, do I need a narrower aperture? Do I have to use the narrow aperture to allow more light to bounce back from all the details in the picture?

These questions plague my mind, since it seems the tutorials on this are always for beginners. Then there are advanced tutorials, which kinda skip this and go straight for the more advanced stuff. The tricky stuff is finding answers to questions which advanced photographers are too embarrassed to ask, and which are unnecessarily complicated for beginners to need to learn. Hopefully I'm making myself clear, it's kinda tricky to explain. Thanks for reading!